Measurement, NAPX9-TLF-CA35 SA v3

Question

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Worked Solution

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Variant 0

DifficultyLevel

760

Question

The rectangular prism, shown below, is cut into 16 identical cubes.



What is the ratio of the surface area of the rectangular prism to the surface area of one of the cubes?

Worked Solution

S.A. of rectangular prism

= 2 × (2s\large s × 2s\large s) + 4 × (4s\large s × 2s\large s)

= 8s\large s2^2 + 32s\large s2^2

= 40s\large s2^2


S.A. of cube

= 6×(s6 × (\large s × s)\large s)

= 6s\large s2^2


∴\therefore Ratio of prism to cube

= 40s\large s2^2 : 6s\large s2^2

= 20 : 3

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
The rectangular prism, shown below, is cut into 16 identical cubes.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX9-TLF-CA35-SA-v3_0-1.svg 300 indent2 vpad
What is the ratio of the surface area of the rectangular prism to the surface area of one of the cubes?
workedSolution
sm_nogap S.A. of rectangular prism >> = 2 × (2$\large s$ × 2$\large s$) + 4 × (4$\large s$ × 2$\large s$) >> = 8$\large s$$^2$ + 32$\large s$$^2$ >> = 40$\large s$$^2$
sm_nogap S.A. of cube >> = $6 × (\large s$ × $\large s)$ >> = 6$\large s$$^2$
sm_nogap $\therefore$ Ratio of prism to cube >> = 40$\large s$$^2$ : 6$\large s$$^2$ >> = {{{correctAnswer}}}
correctAnswer
20 : 3

Answers

Is Correct?Answer
✓

20 : 3

x

18 : 5

x

14 : 9

x

24 : 7

Variant 1

DifficultyLevel

762

Question

The rectangular prism, shown below, is cut into 20 identical cubes.



What is the ratio of the surface area of the rectangular prism to the surface area of one of the cubes?

Worked Solution

S.A. of rectangular prism

= 2 × (2s\large s × 2s\large s) + 4 × (5s\large s × 2s\large s)

= 8s\large s2^2 + 40s\large s2^2

= 48s\large s2^2


S.A. of cube

= 6×(s6 × (\large s × s)\large s)

= 6s\large s2^2


∴\therefore Ratio of prism to cube

= 48s\large s2^2 : 6s\large s2^2

= 8 : 1

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
The rectangular prism, shown below, is cut into 20 identical cubes.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX9-TLF-CA35-SA-v3_1.svg 300 indent2 vpad
What is the ratio of the surface area of the rectangular prism to the surface area of one of the cubes?
workedSolution
sm_nogap S.A. of rectangular prism >> = 2 × (2$\large s$ × 2$\large s$) + 4 × (5$\large s$ × 2$\large s$) >> = 8$\large s$$^2$ + 40$\large s$$^2$ >> = 48$\large s$$^2$
sm_nogap S.A. of cube >> = $6 × (\large s$ × $\large s)$ >> = 6$\large s$$^2$
sm_nogap $\therefore$ Ratio of prism to cube >> = 48$\large s$$^2$ : 6$\large s$$^2$ >> = {{{correctAnswer}}}
correctAnswer
8 : 1

Answers

Is Correct?Answer
x

10 : 3

✓

8 : 1

x

20 : 3

x

14 : 9

Variant 2

DifficultyLevel

758

Question

The rectangular prism, shown below, is cut into 12 identical cubes.



What is the ratio of the surface area of the rectangular prism to the surface area of one of the cubes?

Worked Solution

S.A. of rectangular prism

= 2 × (2s\large s × 2s\large s) + 4 × (3s\large s × 2s\large s)

= 8s\large s2^2 + 24s\large s2^2

= 32s\large s2^2


S.A. of cube

= 6×(s6 × (\large s × s)\large s)

= 6s\large s2^2


∴\therefore Ratio of prism to cube

= 32s\large s2^2 : 6s\large s2^2

= 16 : 3

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
The rectangular prism, shown below, is cut into 12 identical cubes.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX9-TLF-CA35-SA-v3_2.svg 300 indent2 vpad
What is the ratio of the surface area of the rectangular prism to the surface area of one of the cubes?
workedSolution
sm_nogap S.A. of rectangular prism >> = 2 × (2$\large s$ × 2$\large s$) + 4 × (3$\large s$ × 2$\large s$) >> = 8$\large s$$^2$ + 24$\large s$$^2$ >> = 32$\large s$$^2$
sm_nogap S.A. of cube >> = $6 × (\large s$ × $\large s)$ >> = 6$\large s$$^2$
sm_nogap $\therefore$ Ratio of prism to cube >> = 32$\large s$$^2$ : 6$\large s$$^2$ >> = {{{correctAnswer}}}
correctAnswer
16 : 3

Answers

Is Correct?Answer
x

2 : 1

x

8 : 3

✓

16 : 3

x

12 : 1

Variant 3

DifficultyLevel

766

Question

The rectangular prism, shown below, is cut into 24 identical cubes.



What is the ratio of the surface area of the rectangular prism to the surface area of one of the cubes?

Worked Solution

S.A. of rectangular prism

= 2 × (3s\large s × 2s\large s) + 2 × (4s\large s × 2s\large s) + 2 × (4s\large s × 3s\large s)

= 12s\large s2^2 + 16s\large s2^2 + 24s\large s2^2

= 52s\large s2^2


S.A. of cube

= 6×(s6 × (\large s × s)\large s)

= 6s\large s2^2


∴\therefore Ratio of prism to cube

= 52s\large s2^2 : 6s\large s2^2

= 26 : 3

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
The rectangular prism, shown below, is cut into 24 identical cubes.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX9-TLF-CA35-SA-v3_3.svg 330 indent2 vpad
What is the ratio of the surface area of the rectangular prism to the surface area of one of the cubes?
workedSolution
sm_nogap S.A. of rectangular prism >> = 2 × (3$\large s$ × 2$\large s$) + 2 × (4$\large s$ × 2$\large s$) + 2 × (4$\large s$ × 3$\large s$) >> = 12$\large s$$^2$ + 16$\large s$$^2$ + 24$\large s$$^2$ >> = 52$\large s$$^2$
sm_nogap S.A. of cube >> = $6 × (\large s$ × $\large s)$ >> = 6$\large s$$^2$
sm_nogap $\therefore$ Ratio of prism to cube >> = 52$\large s$$^2$ : 6$\large s$$^2$ >> = {{{correctAnswer}}}
correctAnswer
26 : 3

Answers

Is Correct?Answer
✓

26 : 3

x

26: 9

x

361

x

241

Variant 4

DifficultyLevel

768

Question

The rectangular prism, shown below, is cut into 60 identical cubes.



What is the ratio of the surface area of the rectangular prism to the surface area of one of the cubes?

Worked Solution

S.A. of rectangular prism

= 2 × (5s\large s × 3s\large s) + 2 × (4s\large s × 3s\large s) + 2 × (5s\large s × 4s\large s)

= 30s\large s2^2 + 24s\large s2^2 + 40s\large s2^2

= 94s\large s2^2


S.A. of cube

= 6×(s6 × (\large s × s)\large s)

= 6s\large s2^2


∴\therefore Ratio of prism to cube

= 94s\large s2^2 : 6s\large s2^2

= 47 : 3

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
The rectangular prism, shown below, is cut into 60 identical cubes.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX9-TLF-CA35-SA-v3_4.svg 400 indent2 vpad
What is the ratio of the surface area of the rectangular prism to the surface area of one of the cubes?
workedSolution
sm_nogap S.A. of rectangular prism >> = 2 × (5$\large s$ × 3$\large s$) + 2 × (4$\large s$ × 3$\large s$) + 2 × (5$\large s$ × 4$\large s$) >> = 30$\large s$$^2$ + 24$\large s$$^2$ + 40$\large s$$^2$ >> = 94$\large s$$^2$
sm_nogap S.A. of cube >> = $6 × (\large s$ × $\large s)$ >> = 6$\large s$$^2$
sm_nogap $\therefore$ Ratio of prism to cube >> = 94$\large s$$^2$ : 6$\large s$$^2$ >> = {{{correctAnswer}}}
correctAnswer
47 : 3

Answers

Is Correct?Answer
x

6 : 1

x

10 : 3

x

16 : 1

✓

47 : 3

Variant 5

DifficultyLevel

760

Question

The rectangular prism, shown below, is cut into 24 identical cubes.



What is the ratio of the surface area of the rectangular prism to the surface area of one of the cubes?

Worked Solution

S.A. of rectangular prism

= 2 × (2s\large s × 2s\large s) + 4 × (6s\large s × 2s\large s)

= 8s\large s2^2 + 48s\large s2^2

= 56s\large s2^2


S.A. of cube

= 6×(s6 × (\large s × s)\large s)

= 6s\large s2^2


∴\therefore Ratio of prism to cube

= 56s\large s2^2 : 6s\large s2^2

= 28 : 3

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
The rectangular prism, shown below, is cut into 24 identical cubes.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX9-TLF-CA35-SA-v3_5.svg 300 indent2 vpad
What is the ratio of the surface area of the rectangular prism to the surface area of one of the cubes?
workedSolution
sm_nogap S.A. of rectangular prism >> = 2 × (2$\large s$ × 2$\large s$) + 4 × (6$\large s$ × 2$\large s$) >> = 8$\large s$$^2$ + 48$\large s$$^2$ >> = 56$\large s$$^2$
sm_nogap S.A. of cube >> = $6 × (\large s$ × $\large s)$ >> = 6$\large s$$^2$
sm_nogap $\therefore$ Ratio of prism to cube >> = 56$\large s$$^2$ : 6$\large s$$^2$ >> = {{{correctAnswer}}}
correctAnswer
28 : 3

Answers

Is Correct?Answer
x

10 : 1

x

1441

✓

28 : 3

x

5 : 3

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